1
MHT CET 2023 9th May Evening Shift
+2
-0

$$\lim _\limits{x \rightarrow 0} \frac{(1-\cos 2 x) \cdot \sin 5 x}{x^2 \sin 3 x}$$ is

A
$$\frac{10}{3}$$
B
$$\frac{5}{3}$$
C
$$\frac{5}{6}$$
D
$$\frac{2}{3}$$
2
MHT CET 2023 9th May Evening Shift
+2
-0

$$f(x)=\left\{\begin{array}{ll} \frac{1-\cos k x}{x^2}, & \text { if } x \leq 0 \\ \frac{\sqrt{x}}{\sqrt{16+\sqrt{x}}-4}, & \text { if } x>0 \end{array}\right. \text { is continuous at }$$ $$x=0$$, then the value of $$\mathrm{k}$$ is

A
4
B
2
C
$$-$$1
D
$$-$$3
3
MHT CET 2023 9th May Morning Shift
+2
-0

$$\lim _\limits{x \rightarrow \frac{\pi}{2}} \frac{\cot x-\cos x}{(\pi-2 x)^3}$$ equals

A
$$\frac{1}{24}$$
B
$$\frac{1}{16}$$
C
$$\frac{1}{8}$$
D
$$\frac{1}{4}$$
4
MHT CET 2021 21th September Evening Shift
+2
-0

\begin{aligned} & \text { } f(x)=\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x} \text {, if } 1 \leq x<0 \\ & =\frac{2 x+1}{x-2} \quad \text {, if } 0 \leq x \leq 1 \\ \end{aligned}

is continuous in the interval $$[-1,1]$$, then $$p=$$

A
1
B
$$-$$1
C
$$\frac{-1}{2}$$
D
$$\frac{1}{2}$$
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